Question

If 5^x=y and x is positive, which of the following equals 5y^2 in terms of x?

Answer 1

$y=5^x\\\\5y^2=5(5^x)^2=5\cdot5^{x\cdot2}=5^1\cdot5^{2x}=5^{2x+1}\\\\Used:\\\\(a^n)^m=a^{nm}\\\\a^n\cdot a^m=a^{n+m}$

Answer 2

 $5y^2$ is equal to $5^{(2x+1)}$

What is an algebraic expression?

"It is a mathematical statement which consists of variables and constants, and some algebraic operations."

What is an equation?

"It is a mathematical statement which consists of equal symbol between two mathematical statements."

What is exponent?

"It refers to the number of times a number is multiplied by itself."

For given question,

We have been given an equation $5^x=y$

We need to find the value of $5y^2$

$\Rightarrow y = 5^x\\\\\Rightarrow y^2=(5^x)^2\\\\\Rightarrow y^2=5^{2x}\\\\\Rightarrow 5y^2=5\times 5^{2x}\\\\\Rightarrow 5y^2=5^1\times 5^{2x}\\\\\Rightarrow 5y^2=5^{(1+2x)}\\\\\Rightarrow 5y^2=5^{(2x+1)}$

Therefore,  $5y^2$ is equal to $5^{(2x+1)}$

Learn more about the exponents here:

brainly.com/question/12158740

#SPJ2